In [14] nonstandard analysis was used to construct a (standard) global attractor for the 3D stochastic Navier–Stokes equations with general multiplicative noise, living on a Loeb space, using Sell’s approach [26]. The attractor had somewhat ad hoc attracting and compactness properties. We strengthen this result by showing that the attractor has stronger properties making it a neo-attractor – a ...

The asymptotic behavior of solutions of the three-dimensional Navier-Stokes equations is considered on bounded smooth domains with no-slip boundary conditions and on periodic domains. Asymptotic regularity conditions are presented to ensure that the convergence of a Leray-Hopf weak solution to its weak ω-limit set (weak in the sense of the weak topology of the space H of square-integrable diver...

In this article, we study the structure of global attractor for a non-local one-dimensional quasilinear problem. The strong relation our problem with version Chafee-Infante allows us to describe its attractor. For that, made use Conley index and connection matrix theories in order find geometric information such as existence heteroclinic connections between equilibria. way, is completely descri...